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Simplifying 450000 = 0.4x2 + 10x + 50 Reorder the terms: 450000 = 50 + 10x + 0.4x2 Solving 450000 = 50 + 10x + 0.4x2 Solving for variable 'x'. Combine like terms: 450000 + -50 = 449950 449950 + -10x + -0.4x2 = 50 + 10x + 0.4x2 + -50 + -10x + -0.4x2 Reorder the terms: 449950 + -10x + -0.4x2 = 50 + -50 + 10x + -10x + 0.4x2 + -0.4x2 Combine like terms: 50 + -50 = 0 449950 + -10x + -0.4x2 = 0 + 10x + -10x + 0.4x2 + -0.4x2 449950 + -10x + -0.4x2 = 10x + -10x + 0.4x2 + -0.4x2 Combine like terms: 10x + -10x = 0 449950 + -10x + -0.4x2 = 0 + 0.4x2 + -0.4x2 449950 + -10x + -0.4x2 = 0.4x2 + -0.4x2 Combine like terms: 0.4x2 + -0.4x2 = 0.0 449950 + -10x + -0.4x2 = 0.0 Begin completing the square. Divide all terms by -0.4 the coefficient of the squared term: Divide each side by '-0.4'. -1124875 + 25x + x2 = 0 Move the constant term to the right: Add '1124875' to each side of the equation. -1124875 + 25x + 1124875 + x2 = 0 + 1124875 Reorder the terms: -1124875 + 1124875 + 25x + x2 = 0 + 1124875 Combine like terms: -1124875 + 1124875 = 0 0 + 25x + x2 = 0 + 1124875 25x + x2 = 0 + 1124875 Combine like terms: 0 + 1124875 = 1124875 25x + x2 = 1124875 The x term is 25x. Take half its coefficient (12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. 25x + 156.25 + x2 = 1124875 + 156.25 Reorder the terms: 156.25 + 25x + x2 = 1124875 + 156.25 Combine like terms: 1124875 + 156.25 = 1125031.25 156.25 + 25x + x2 = 1125031.25 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 1125031.25 Calculate the square root of the right side: 1060.674903069 Break this problem into two subproblems by setting (x + 12.5) equal to 1060.674903069 and -1060.674903069.Subproblem 1
x + 12.5 = 1060.674903069 Simplifying x + 12.5 = 1060.674903069 Reorder the terms: 12.5 + x = 1060.674903069 Solving 12.5 + x = 1060.674903069 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = 1060.674903069 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 1060.674903069 + -12.5 x = 1060.674903069 + -12.5 Combine like terms: 1060.674903069 + -12.5 = 1048.174903069 x = 1048.174903069 Simplifying x = 1048.174903069Subproblem 2
x + 12.5 = -1060.674903069 Simplifying x + 12.5 = -1060.674903069 Reorder the terms: 12.5 + x = -1060.674903069 Solving 12.5 + x = -1060.674903069 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = -1060.674903069 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -1060.674903069 + -12.5 x = -1060.674903069 + -12.5 Combine like terms: -1060.674903069 + -12.5 = -1073.174903069 x = -1073.174903069 Simplifying x = -1073.174903069Solution
The solution to the problem is based on the solutions from the subproblems. x = {1048.174903069, -1073.174903069}
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